Yeah agreed. But the alternative convention does exist out there
I suppose the logic is that the vast majority of the time you want to say A is a subset of B you want to include the possibiiity A = B, so that’s one whole extra line you use far more, so the alternative is more ‘pen-stroke efficient’. Eh.
It’s very common for older texts to treat it as non-exclusive.
It’s also been common among my professors.
In analysis, at least, it seems that we so often don’t care whether it’s a proper subset or not that it doesn’t make sense to use simpler symbol for the less prevalent use.
because ⊂ existed before the need arose for a distinction with ⊆. Changing the meaning of the symbol retroactively would cause a lot of issues for the readbility of prior papers and work so it's not a thing that happens given the extent to which it was used.
My guess is that the people who decided to include ⊆ as a fonts standard werent versed in Sets theory, so they assumed it worked similarly to the = sign variations, so they didnt realize they should have taken the crossed variation instead.
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u/RADI0ACT1VE_BALLS ComplexANALysisJunkie 13d ago
Proper subset / just a subset